Preheat the oven to 400 degrees F.
Coat a 9x13-inch baking dish with nonstick cooking spray.
In a medium saucepan over medium-high heat, add the broth, the rice, the soy sauce, and the thyme and stir to combine.
Bring the broth mixture to a boil.
Cover the saucepan and reduce the heat to low.
Simmer the broth mixture until the rice is tender and the broth is absorbed, about 20 minutes.
Remove and discard the thyme sprigs, then set the rice mixture aside.
In a small bowl, add 1/2 cup of the pepper jack cheese, the crushed crackers, and 2 tablespoons of the melted butter and stir to combine. Set the crumb topping aside.
In a large stockpot over medium heat, melt the remaining butter.
Add the bell peppers, the poblanos, the onions, and the black pepper to the melted butter and cook, while stirring, until the vegetables are tender, about 5 minutes.
Add the garlic and cook, while stirring, until fragrant, about 30 seconds-1 minute.
Add the flour to the vegetable mixture and cook, while whisking or stirring, until the raw flour smell disappears, about 2-3 minutes.
Slowly add the milk to the vegetable mixture, while whisking constantly.
Cook the vegetable mixture, while stirring frequently, until thickened and smooth, about 3-4 minutes.
Add the remaining pepper jack cheese, the sour cream, and the salt to the vegetable mixture and stir to combine.
Add the rice mixture, the ham, and the peas to the vegetable mixture and stir to combine.
Add the rice mixture to the prepared pan, spreading it out evenly.
Sprinkle the rice mixture with the crumb topping.
Bake until the casserole is bubbly and the topping is golden-brown, about 15-20 minutes.
Let the casserole stand for 5 minutes.
Serve garnished with the parsley.